1. You can link the website address on your website.

2. I will paste the link on the messanger, and will send you the address.
(Are the sentences above grammatical? Would you check them? Thank you.)

1 is OK, but I'd write it like this: You can include the URL on your website.

2. I don't know what "the messenger" is. Please explain.

Yes, the sentences you provided are grammatically correct. However, there are a few minor revisions that could improve clarity:

1. You can include a website address/link on your website.
2. I will paste the link in the messenger and send you the address.

These revisions maintain the same meaning while improving fluency and readability.